Challenge Level

*In this problem, you may find it useful to draw some examples on printable sets of circle templates.*

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Can you work systematically to prove this?

Now try changing the number of points round the edge.

Can you do it now?

Can you show by calculation that the angle is a right angle?

What do you notice about the side of the triangle opposite the right angle?

Try this with other numbers of points round the edge.

When is it possible to make a right-angled triangle?

In this interactivity, the points are equally spaced around a circle. Imagine that they are not.

Can you explain the conditions which will give a right-angled triangle?

Can you prove this?

Many thanks to Geoff Faux who introduced us to the merits of the 9 pin circular geo-board.